Single email daily limits for messages sent using API methods

What are the single email limits we can send from a trigger, apex class or API?

Where can I view how many emails our org has remaining on any given day?

If I invoke the 'reserveSingleEmailCapacity()' method from a trigger before sending the email, am I able to catch this exception and save the record?

Using 'reserveSingleEmailCapacity()' raises a System exception, so if you've reached the capacity you are not able to save the record.

Notes:

• All recipients in the 'To', 'Cc' and 'BCC' fields count against the limit for email sent using Apex or the API. For example, an email with 2 addresses in the 'To' field and 1 address in the 'CC' field would count as 3 calls. BCC emails added via Compliance BCC Email are not counted against the limit.
• Emails sent using 'setTargetObjectId()' set aginst the User object do not count against the 'SingleEmailMessage' limit.
• Trial organizations are set to a default of 15 and NOT 5000. If you already have a contract with us for a full Salesforce environment, we can increase this limit to the standard 5000. As a general guideline, we do recommend that you complete your primary testing in Sandbox or Developer Environments if you already have a contract. Please contact Support to have this increased if needed.